Do a hypothesis test for several random samples from the same normally distributed population and count the number of times a Type I error is made.
We will use a calculator to generate random samples of size 5 and do a small sample t-test to test the hypothesis. The samples will be taken from a population with a normal distribution with a mean of 100 and a standard deviation of 15.
1) What is the definition of a type I error?
2) Explain the meaning of ?=0.10 in terms of type I or type II errors.
3) Each member of the group should generate at least 10 sets of data and do a hypothesis test on each set of data. You do not need to do the requirement check or state the conclusion. Detailed instructions are at the end of the instructions. Combine the results from the whole group. The group should have at least 30 sets of data. Include the table of all the data in your write-up.
4) For what percentage of the samples did you reject the null hypothesis?
5) The population mean in this problem really is 100 because of the way we set up the calculator so the null hypothesis is true. We are testing the claim that the mean is not 100 so we should fail to reject the null hypothesis each time. A "reject" means we are rejecting the null hypothesis when it is true. This is a type I error. What percentage of the time did you make a type I error? (What is the percentage you just calculated?)